The 19-year-old enjoyed a breakout tournament at the World Cup to earn a reported £10 million switch to Anfield, though he will be immediately loaned back to Lille for the upcoming season.
Goal reported in June that the club were closing in on the signing of Origi, Dejan Lovren and Lazar Markovic - with the Belgian the last of the trio to have his move finalised.
"I am very, very happy and delighted a club as big as Liverpool showed interest in me. I'm very excited," said the Belgian teenager.
"I know it's a club with a great history, great fans and a lot of great players. For me, Liverpool is one of the greatest clubs in the world and I'm very excited to be part of this great history."
Tottenham were reportedly showing interest in bringing Origi to White Hart Lane but Goal understands these claims were wide of the mark.